Interior coating does work to a degree to slow the heat transferring from the interior to the exterior. My brother is into the B.O.P. cars from the 60's, and the exhaust ports on those cylinder heads hangs out past the main body of the cylinder head. They are notorious for having the paint burn off due to all that heat building up in the head where the exhaust manifolds bolt to. On some of the engines he has rebuilt he sprayed the inside of the exhaust ports with silver vht header paint, and it has made the paint actually stay on the head. It does discolor the paint slightly, but the paint does not turn black and flake off like they normally do as seen in the link below. Coated on both sides would help with heat for sure, but if you told me to pick only one side I say interior, and leave the outside raw so stains and scratches are easier to deal with. That is the real benefit of using SS to me is it's lower maintenance vs the coatings.

Typical no paint left on the exhaust ports example. https://www.ebay.com/itm/175034846761

Having owned many dirtbikes whatever they use for exhaust tubing is the best thing going Might be Ti? Anyways, it never rusts and even the nastiest crud washes off with a little help from an SOS soap pad.